Discrete Mathematics Final Exam Study Guide, Exams of Discrete Mathematics

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Discrete Mathematics

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Discrete Mathematics Final Exam Study Guide

1. edges connect the vertices by lines or curves
2. vertices diagram of dots
3. degree # of times an edge touches it
4. indegree # of edges coming into the vertex
5. outdegree # of edges going out of the vertex
6. directed graph Uses arrows
7. undirected graph Graph that does not use arrows and is not directed
8. coloring An assignment of different values(colors) to each vertex such that no 2 vertices of the same color share an edge
9. planar graph If the graph can be written down without any edges cross- ing each other
10. Complete graph A simple graph in which every pair of vertices is connected by an edge
11. connected graph An undirected graph; if there is a path connecting any 2 vertices 12.Tip about euler circuits 13.Tip about euler paths If all the vertices have an even degree, then it is a euler circuit. If a graph has more than two vertices of odd degree, then there is no euler path.
12. set a collection of elements
13. equal sets Sets containing the same elements
14. subsets Sets that exist within a larger set
15. empty set A set with no elements shown by the symbol { } or Ø, and is a subset of every set as well

Discrete Mathematics Final Exam Study Guide

functions out of old ones.

3 / 4 27.Show that two sets have equal cardinality by describing a one-to-one corre- spondence 28.What does it mean to be a re- flexive relation? 29.Example of a re- flexive binary re- lation 30.What does it mean to be a symmetric rela- tion? 31.Example of a symmetric bina- ry relation 32.What does a transitive rela- tion look like? 33.Example of a transitive rela- tion By showing that the function is bijective, this means that the function is both onto and one-to- one. This means that f(x) = y, and that f(a) = b. By showing this, the cardinality is the same, since a bijective function shows a perfect pairing. Ex: X: {1,2,3}, Y: {4,5,6} aRa ( a is related to itself) Each element is related to itself. If even one element is not related to itself, then it is NOT reflexive. This is usually seen as loops on a graph {(1,1), (2,2), (2,3), (3,2), (3,3), (3,4), (4,3), (5,5), (4,4)} This shows a reflexive relation For a relation to be symmetric, aRb and bRa. Basically, this means that a is related to b, and b is related to a, which shows symmetry. R3= {(1,3), (1,5), (2,4), (3,1), (3,5), (4,2), (5,1), (5,3)} This shows a symmetric relation aRb and bRc, then aRc. If a is related to b, and b is related to c, then a is ALSO related to C. R2: {(1,2), (1,4), (1,5), (2,4), (2,5), (3,4), (3,5), (4,5), (4,4)}

1. Statistics It is the science of collecting, organizing, summarizing, and analyzing information to draw conclusion. 2. Descriptive Statis- **tics
2. Inferential Statis-** tics Collecting, summarizing, presenting and analyzing an entire set of collected data. Using data collected from a small group to draw conclu- sions about a larger group.
3. Central Tendency It is the extent to which the data values group around a typical or central value.
4. Mean It is the sum of the data values divided by the number of data values. It is also called the average. It is appropriate only for data under interval and ratio scale measure- ment
5. Median In an ordered array, it is the "middle" number. It divides the distribution into two equal parts.
6. Mode It is the value that occurs most often.
7. Correlation It is used to test relationships between two variables. 9. Correlation Analy- sis The study of how variables are correlated is.
8. Dependent Variable It is something that depends on other factors. 11.Independent Vari- able 12.Correlation Coeffi- cient 13.Regression Analy- sis

It is not changed by the other variables you are trying to measure It is a number that describes how close to a linear relationship there is between two variables. It predicts the value of a dependent variable based on the value of at least one independent variable

14. Regression Line It is used to model the relationship of variables

It contains of two or more statement with connective. It involve terms such as all, each, every, no, none, some, here exists, and at least one.

It is either include or exclude every element of the universal set. These includes all, each, every, no, and none.

31. Existential Quanti- It claims the existence of something but don't include fiers the entire universal set. These are some, there exists, at least one.
32. Negation It is a corresponding statement with the opposite truth value.
33. Truth Tables It displays the relationships between the truth values of statements or propositions.
34. Conjuction The propositions of p and q is the compound statement "p and q" denoted as p ‘ q which is true only when both p and q are true, otherwise, is false.
35. Disjunction The propositions of p and q is the compount statement "p and q" denoted as p “ q which is false only when both p and q are false, otherwise, is true.
36. Conditional The propositions p and q is the compound statement "if p, then q." denotef by p ’ q which is false only when p is true and q is false.
37. Biconditional The propositions p and q is the statement "p if and only if q." denoted as p •’ q which is true only when both p and

41. Grouping Symbols These are used to associate groups of numbers and operators.
42. Variables These are letters that represent quantities.
43. Language It is a systematic means of communicating by the use of sounds or conventional symbols. 44.Numbers, Sets, Functions, & Per- form Operations The Mathematical Language was created/designed with:
44. Numbers These are the very first symbols that can be use to represent quantity.
45. Operation Symbols It can act as connectives in mathematical sentences
46. Not The symbol ~ represents a negation. What does it mean?

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